WASHINGTON—The White House said Saturday it was concerned by what it called a "concerted campaign" by pro-Russian separatists to stoke tensions in eastern Ukraine, warning Russian President Vladimir Putin against using the events there as a pretext for seizing more Ukrainian territory.

In a phone call Saturday, U.S. Secretary of State John Kerry expressed his concern with Russian Foreign Minister Sergei Lavrov, the State Department said. Mr. Kerry made clear that if Russia doesn't take action to de-escalate and...